A069779 q-factorial numbers 4!_q.

1, 24, 315, 2080, 8925, 29016, 77959, 182400, 384345, 746200, 1356531, 2336544, 3847285, 6097560, 9352575, 13943296, 20276529, 28845720, 40242475, 55168800, 74450061, 99048664, 130078455, 168819840, 216735625, 275487576, 346953699, 433246240, 536730405, 660043800

Offset: 0

Author

Franklin T. Adams-Watters, Apr 07 2002

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A069777-A069778, A218503.

Programs

Mathematica

Table[QFactorial[4, n], {n, 0, 29}] (* Arkadiusz Wesolowski, Nov 01 2012 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,24,315,2080,8925,29016,77959},30] (* Harvey P. Dale, Aug 30 2020 *)

Formula

a(n) = (n + 1)*(n^2 + n + 1)*(n^3 + n^2 + n + 1).

G.f.: (1 + 17*x + 8*x^2*(21 + 43*x) + 5*x^4*(35 + 3*x))/(1 - x)^7. - Arkadiusz Wesolowski, Nov 01 2012